The Theory of Probability: Explorations and Applications

From classical foundations to advanced modern theory, this self-contained and comprehensive guide to probability weaves together mathematical proofs, historical context and richly detailed illustrative applications. A theorem discovery approach is used throughout, setting each proof within its historical setting and is accompanied by a consistent emphasis on elementary methods of proof. Each topic is presented in a modular framework, combining fundamental concepts with worked examples, problems and digressions which, although mathematically rigorous, require no specialised or advanced mathematical background. Augmenting this core material are over 80 richly embellished practical applications of probability theory, drawn from a broad spectrum of areas both classical and modern, each tailor-made to illustrate the magnificent scope of the formal results. Providing a solid grounding in practical probability, without sacrificing mathematical rigour or historical richness, this insightful book is a fascinating reference and essential resource, for all engineers, computer scientists and mathematicians.

Table of Contents

Part A: ELEMENTS
I Probability Spaces
II Conditional Probability
III A First Look at Independence
IV Probability Sieves
V Numbers Play a Game of Chance
VI The Normal Law
VII Probabilities on the Real Line
VIII The Bernoulli Schema
IX The Essence of Randomness
X The Coda of the Normal

Part B: FOUNDATIONS
XI Distribution Functions and Measure
XII Random Variables
XIII Great Expectations
XIV Variations on a Theme of Integration
XV Laplace Transforms
XVI The Law of Large Numbers
XVII From Inequalities to Concentration
XVIII Poisson Approximation
XIX Convergence in Law, Selection Theorems
XX Normal Approximation

Part C: APPENDIX
XXI Sequences, Functions, Spaces